An ever-increasing number of relatively inexpensive, low power wireless data communication services, networks and devices have been made available over the past number of years, promising near wire speed transmission and reliability. Various wireless technology is described in detail in the 802 IEEE Standards, including for example, the IEEE Standard 802.11a (1999) and its updates and amendments, the IEEE Standard 802.11g (2003), and the IEEE Standard 802.11n now in the process of being adopted, all of which are collectively incorporated herein fully by reference. These standards have been or are in the process of being commercialized with the promise of 54 Mbps or higher data rate, making them a strong competitor to traditional wired Ethernet and the more common “802.11b” or “WiFi” 11 Mbps mobile wireless transmission standard.
Generally speaking, transmission systems compliant with the IEEE 802.11a and 802.11g or “802.11a/g” standards as well as the IEEE 802.11n standard achieve their high data transmission rates using Orthogonal Frequency Division Multiplexing (OFDM) encoded symbols. Generally speaking, the use of OFDM divides the overall system bandwidth into a number of frequency sub-bands or channels, with each frequency sub-band being associated with a respective sub-carrier. Data upon each sub-carrier may be modulated with a modulation scheme such as QAM, phase shift keying, etc. Thus, each frequency sub-band of the OFDM system may be viewed as an independent transmission channel within which to send data, thereby increasing the overall throughput or transmission rate of the communication system.
Generally, transmitters used in the wireless communication systems that are compliant with the aforementioned 802.11a/802.11g/802.11n standards as well as other standards such as the 802.16 IEEE Standard, perform multi-carrier OFDM symbol encoding (which may include error correction encoding and interleaving), convert the encoded symbols into the time domain using Inverse Fast Fourier Transform (IFFT) techniques, and perform digital to analog conversion and conventional radio frequency (RF) upconversion on the signals. These transmitters then transmit the modulated and upconverted signals after appropriate power amplification to one or more receivers, resulting in a relatively high-speed time domain signal with a large peak-to-average ratio (PAR).
Likewise, the receivers used in the wireless communication systems that are compliant with the aforementioned 802.11a/802.11g/802.11n and 802.16 IEEE standards generally include an RF receiving unit that performs RF downconversion and filtering of the received signals (which may be performed in one or more stages), and a baseband processor unit that processes the OFDM encoded symbols bearing the data of interest. Generally, the digital form of each OFDM symbol presented in the frequency domain is recovered after baseband downconversion, conventional analog to digital conversion and Fast Fourier Transformation of the received time domain analog signal. Thereafter, the baseband processor performs frequency domain equalization (FEQ) and demodulation to recover the transmitted symbols. The recovered and recognized stream of symbols is then decoded, which may include deinterleaving and error correction using any of a number of known error correction techniques, to produce a set of recovered signals corresponding to the original signals transmitted by the transmitter.
For ease of explanation, in the examples presented herein, streams and symbols have a one-to-one correspondence. That is, a single stream is associated with a single symbol and vice versa. Accordingly, the words “streams” and “symbols” may be used interchangeably. However, it should be understood that a given stream, for example, may have a number of associated symbols and vice versa.
In wireless communication systems, the RF modulated signals generated by the transmitter may reach a particular receiver via a number of different propagation paths, the characteristics of which typically change over time due to the phenomena of multi-path and fading. Moreover, the characteristics of a propagation channel differ or vary based on the frequency of propagation. To compensate for the time varying, frequency selective nature of the propagation effects, and generally to enhance effective encoding and modulation in a wireless communication system, each receiver of the wireless communication system may periodically develop or collect channel state information (CSI) for each of the frequency channels, such as the channels associated with each of the OFDM sub-bands discussed above. Generally speaking, CSI is information defining or describing one or more characteristics about each of the OFDM channels (for example, the gain, the phase and the SNR of each channel). Upon determining the CSI for one or more channels, the receiver may send this CSI back to the transmitter, which may use the CSI for each channel to precondition the signals transmitted using that channel so as to compensate for the varying propagation effects of each of the channels.
To further increase the number of signals which may be propagated in the communication system and/or to compensate for deleterious effects associated with the various propagation paths, and to thereby improve transmission performance, it is known to use multiple transmit and receive antennas within a wireless transmission system. Such a system is commonly referred to as a multiple-input, multiple-output (MIMO) wireless transmission system and is specifically provided for within the 802.11n IEEE Standard now being adopted. Various other standards and projects, such as the 802.16 standard, or WiMAX, and the Long Term Evolution (LTE) project, support MIMO techniques. Generally speaking, the use of MIMO technology produces significant increases in spectral efficiency and link reliability of IEEE 802.11, IEEE 802.16, and other systems, and these benefits generally increase as the number of transmit and receive antennas within the MIMO system increases.
In addition to the frequency sub-channels created by the use of OFDM, a MIMO channel formed by the various transmit and receive antennas between a particular transmitter and a particular receiver may include a number of independent spatial channels. As is known, a wireless MIMO communication system can provide improved performance (e.g., increased transmission capacity) by utilizing the additional dimensionalities created by these spatial channels for the transmission of additional data. Of course, the spatial channels of a wideband MIMO system may experience different channel conditions (e.g., different fading and multi-path effects) across the overall system bandwidth.
Generally, a wireless communication system in which a transmitting device transmits a signal to a receiving device may be represented by a model such as:y=hx+z,  (1)where y represents the symbol, or symbols, received by the receiving device, h represents the communication channel (also referred to as “channel gain”), x represents the symbol, or symbols transmitted by the transmitting device and z represents noise (e.g., additive Gaussian noise with power σz2). Therefore, when a receiving device receives a symbol y, the receiving device may estimate the symbol x transmitted by the transmitting device.
The receiving device may estimate the transmitted symbol x using various techniques including “hard-decision” techniques and “soft-decision” techniques. Hard techniques typically involve simply making a determination regarding values of bits in the transmitted symbol x (e.g., whether a given transmitted bit is 0 or 1). Soft-decision techniques typically involve calculating likelihood values for the transmitted bits, where a likelihood value for a given bit indicates whether that bit is more likely to be 0 or 1. For example, the likelihood value L(i) for a given bit i in the transmitted symbol x may be represented by a log-likelihood ratio (LLR) as follows:
                              L          ⁡                      (            i            )                          =                  log          ⁢                                    P              ⁡                              (                                  i                  =                  1                                )                                                    P              ⁡                              (                                  i                  =                  0                                )                                                                        (        2        )            
where P(i=1) is the probability that the bit i is equal to 1 and P(i=0) is the probability that the bit i is equal to 0. Accordingly, if L(i) is a relatively large positive number, the probability that the bit i is equal to 1 is much greater than the probability that the bit i is equal to 0, and it may be determined that the bit i is equal to 1. Likewise, if L(i) is a relatively large negative number, the probability that the bit i is equal to 0 is much greater than the probability that the bit i is equal to 1, and it may be determined that bit i is equal to 0. If L(i) is neither a large positive number nor a large negative number, additional processing may be necessary to estimate the value of the bit i.
As known in the art, the LLR calculation for the bit i expressed in equation (2) may be written as follows:
                              L          ⁡                      (            i            )                          =                              log            ⁢                                                            ∑                                      x                    ∈                                          S                                              1                        ,                        i                                                                                            ⁢                                  s                                                            -                                                                                                                              y                            -                            hx                                                                                                    2                                                                                    σ                      z                      2                                                                                                                    ∑                                      x                    ∈                                          S                                              0                        ,                        i                                                                                            ⁢                                  e                                                            -                                                                                                                              y                            -                            hx                                                                                                    2                                                                                    σ                      z                      2                                                                                                    =                                    log              ⁢                                                ∑                                      x                    ∈                                          S                                              1                        ,                        i                                                                                            ⁢                                  e                                                            -                                                                                                                              y                            -                            hx                                                                                                    2                                                                                    σ                      z                      2                                                                                            -                                          ∑                                  x                  ∈                                      S                                          0                      ,                      i                                                                                  ⁢                              e                                                      -                                                                                                                    y                          -                          hx                                                                                            2                                                                            σ                    z                    2                                                                                                          (        3        )            
where S1,i is a set of all possible data symbols x with the bit i equal to 1 and S0,i is a set of all possible data symbols x with the bit i equal to 0. As is also known in the art, equation (3) may be approximated using log-max approximation as follows:
                              L          ⁡                      (            i            )                          ≈                                            min                              x                ∈                                  S                                      0                    ,                    i                                                                        ⁢                                                                            y                  -                  hx                                                            2                                -                                    min                              x                ∈                                  S                                      1                    ,                    i                                                                        ⁢                                                                            y                  -                  hx                                                            2                                                          (        4        )            
As indicated by equation (4), the LLR calculation for a given bit i in the transmitted symbol x depends, in part, on the estimated communication channel h. Various techniques may be used to estimate the communication channel h. However, these techniques will typically estimate the communication channel h with some degree of error. As a result, LLR based on h may lead to errors in estimating x.